TY - JOUR
T1 - Some Inplace Identities for Integer Compositions
AU - Munagi, Augustine O.
AU - Sellers, James A.
N1 - Publisher Copyright:
© 2015 NISC (Pty) Ltd.
PY - 2015/7/4
Y1 - 2015/7/4
N2 - In this paper, we give two new identities for compositions, or ordered partitions, of integers. These two identities are based on closely-related integer partition functions which have recently been studied. Thanks to the structure inherent in integer compositions, we are also able to extensively generalize both of these identities. Bijective proofs are given and generating functions are provided for each of the types of compositions which arise. A number of arithmetic properties satisfied by the functions which count such compositions are also highlighted.
AB - In this paper, we give two new identities for compositions, or ordered partitions, of integers. These two identities are based on closely-related integer partition functions which have recently been studied. Thanks to the structure inherent in integer compositions, we are also able to extensively generalize both of these identities. Bijective proofs are given and generating functions are provided for each of the types of compositions which arise. A number of arithmetic properties satisfied by the functions which count such compositions are also highlighted.
UR - http://www.scopus.com/inward/record.url?scp=84943200508&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84943200508&partnerID=8YFLogxK
U2 - 10.2989/16073606.2014.981731
DO - 10.2989/16073606.2014.981731
M3 - Article
AN - SCOPUS:84943200508
SN - 1607-3606
VL - 38
SP - 535
EP - 540
JO - Quaestiones Mathematicae
JF - Quaestiones Mathematicae
IS - 4
ER -